Introduction to Gravitation and Newtonian Mechanics

Nature of the Force: Gravitational force is defined as a universal force. It does not only exist between two objects on the Earth but also acts between any two objects in the entire universe.
Discovery of Gravitation: The phenomenon was discovered by Sir Isaac Newton.
The Newton Apple Anecdote:
- Newton discovered the force after observing an apple fall from a tree toward the ground.
- His observation led to several investigative questions:
  - Why do all apples fall vertically downward rather than at an angle to the vertical?
  - Why do apples not fly off in a horizontal direction?
Newton's Conclusion on Attraction: After deliberation, Newton concluded that the Earth must be attracting the apple toward itself.
Direction of Force: The attractive force exerted by the Earth is directed specifically toward the center of the Earth.
The Definition of Vertical Direction: The direction from the apple on the tree to the center of the Earth is defined as the vertical direction at that specific position. Consequently, the apple falls vertically downwards.
Geometric Orientation: The force on an object (such as an apple) on a tree is directed toward the center of the Earth, which is along the perpendicular from the position of the object to the surface of the Earth.

Heights and Distances: Gravitational force acts on objects at different heights from the surface of the Earth.
Celestial Application: The force of gravity extends beyond terrestrial objects to celestial bodies at much greater distances.
- Earth and the Moon: Gravitational force exists between the Earth and the Moon.
- Solar System Extension: Newton hypothesized that the force acts on even more distant objects, including other planets and the Sun.

Role of Force in Motion: A force is a necessary requirement to change both the speed and the direction of motion of an object.